German Patent 21 56 011 has already described a cap for dispensing a fluid or viscous product, intended for being mounted on the neck of a container containing the product. The cap includes a short tube that comes to be fixed on the neck and is closed by a horizontal top associated with a nozzle projecting from the side opposite the short tube, and the nozzle communicates with the interior of the container, and the cap also includes passageway means for dispensing the product to the outside and means for closing and opening the passageway means. The opening means includes a lid in the form of a small plate, mounted pivotably about an axis substantially orthogonal to that of the short tube, the lid being arranged to close the nozzle for a closed position, and the passageway means include a conduit which is provided in the lid and discharges to outside the lid and communicates with the nozzle.